Which of the following numbers is a factor of 110? ${3,8,10,13,14}$
Answer: By definition, a factor of a number will divide evenly into that number. We can start by dividing $110$ by each of our answer choices. $110 \div 3 = 36\text{ R }2$ $110 \div 8 = 13\text{ R }6$ $110 \div 10 = 11$ $110 \div 13 = 8\text{ R }6$ $110 \div 14 = 7\text{ R }12$ The only answer choice that divides into $110$ with no remainder is $10$ $ 11$ $10$ $110$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $10$ are contained within the prime factors of $110$ $110 = 2\times5\times11 10 = 2\times5$ Therefore the only factor of $110$ out of our choices is $10$. We can say that $110$ is divisible by $10$.